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The Cherenkov wakes excited by intense laser drivers in a perpendicularly magnetized plasma are a potential source of high-power terahertz radiation. We present a two-dimensional (2D) theory of the emission of magnetized wakes excited by a short laser pulse. The 2D model reveals the important role of the transverse size of the laser pulse missed in previous simple one-dimensional estimations of the radiation. We derived expressions for the radiated fields and for the angular/frequency distribution of the radiated energy. Beats in the radiation pattern behind the moving pulse are predicted and explained. For the interpretation of existing experimental results, the time dependence of the energy flux parallel and perpendicular to the laser path is examined.